The FREQ Procedure

Example 9: Testing Marginal Homogeneity with Cochran's Q

Procedure features:

TABLES statement, multiple requests

TABLES statement options:

	AGREE
	NOCUM
	NOPRINT

WEIGHT statement

Other features:

FORMAT procedure

This example

creates frequency tables for the analysis variables using existing cell counts
computes tests and measures of agreement, which include Cochran's Q statistic for stratified 2×2 contingency tables
suppresses the cumulative frequencies and cumulative percentages
suppresses the display of contingency tables.

When a binary response is measured several times or under different conditions, Cochran's Q tests that the marginal probability of a positive response is unchanged across the times or conditions. When there are more than two response categories, you can use PROC CATMOD in SAS/STAT software to fit a repeated-measures model. Data for this example are from Categorical Data Analysis by Alan Agresti. Copyright © 1990. Reprinted by permission of John Wiley and Sons, Inc.

Program

options nodate pageno=1 linesize=80 pagesize=60; proc format; value $responsefmt 'F'='Favorable' 'U'='Unfavorable'; run;

data drugs; input Drug_A $ Drug_B $ Drug_C $ Count @@; datalines; F F F 6 F F U 16 F U F 2 F U U 4 U F F 2 U F U 4 U U F 6 U U U 6 ;

proc freq data=drugs; weight count;

tables drug_a drug_b drug_c/nocum;

tables drug_a*drug_b*drug_c/agree noprint;

format drug_a drug_b drug_c $responsefmt.; title 'Study of Three Drug Treatments for a Chronic Disease'; run;

Output

The one-way frequency tables provides the marginal response for each drug. For drugs A and B, 61% of the subjects reported a favorable response while 35% of the subjects reported a favorable response for drug C.

McNemar's test shows strong discordance between drugs B and C when the response to drug A is favorable. A small negative value of simple kappa indicates no agreement between the drug B response and the drug C response.
In this example, the hypothesis of interest is whether the response to treatment is equal for the three drugs. Cochran's Q is statistically significant (p=.014), which leads to rejection of the null hypothesis that the probability of favorable response is the same for the three drugs.

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The one-way frequency tables provides the marginal response for each drug. For drugs A and B, 61% of the subjects reported a favorable response while 35% of the subjects reported a favorable response for drug C.